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# Cell phones

Alignments to Content Standards: F-IF.A.2

Let $f(t)$ be the number of people, in millions, who own cell phones $t$ years after 1990. Explain the meaning of the following statements.

1. $f(10)=100.3$
2. $f(a) = 20$
3. $f(20) = b$
4. $n=f(t)$

## IM Commentary

This simple task assesses whether students can interpret function notation. The four parts of the task provide a logical progression of exercises for advancing understanding of function notation and how to interpret it in terms of a given context.

## Solution

1. The number of people who own cell phones in the year 2000 is $100,\!300,\!000$.
2. There are $20,\!000,\!000$ people who own cell phones $a$ years after 1990.
3. There will be $b$ million people who own cell phones in the year 2010.
4. The number $n$ is the number of people (in millions) who own cell phones $t$ years after 1990.

almost 4 years

#### Cam says:

almost 4 years

Excellent points and suggestions -- thanks for the comment!

#### Peter says:

almost 4 years

I'm constructing a scoring rubric for items like this. Does the following seem reasonable? (It's for part C.) I'd appreciate comments & suggestions.

(3 pts) There will be b million people who own cell phones in the year 2010.

(-1 pt) Incorrect units for function value, such as “There will be b people who own cell phones in the year 2010.”

(-1 pt) Unsimplified variable, such as “There will be b million people who own cell phones 20 years after 1990.”

#### Cam says:

almost 4 years

I personally hesitate to give feedback on rubrics without knowing things like the intent of the assessment, how it will be used, etc. That said, I think penalizing students so much for the two (-1 pt) options seems extreme -- a student answering the first question actually does have a reasonably good understanding of function notation, which is the point of the exercise. I would give that 2 out of 3. Ditto for the other (-1) pt one, if not full credit -- they haven't made a single mathematical error, or arguably, no error at all. It seems quite surprising to me that you would think either of those answers less valuable than "no substantial answer".

#### Jennifer Lingle says:

Used this simple task with my 8th graders enrolled in High School Math II. It was the single best way I have ever reviewed function notation. And they came away absolutely understanding input, output, x, f(x), independent and dependent variables and how all of those terms are connected. It was fabulous.